控制Logistic系统的自适应Chebyshev多项式神经网络算法  

Algorithm for controlling logistic system using adaptive chebyshev polynomials neural networks

作　　者：李目[1,2] 谭文[1] 何怡刚[2] 周少武[1] 

机构地区：[1]湖南科技大学信息与电气工程学院,湘潭411201 [2]湖南大学电气与信息工程学院,长沙410082

出　　处：《电子测量与仪器学报》2010年第8期730-736,共7页Journal of Electronic Measurement and Instrumentation

基　　金：湖南省自然科学基金重点(编号:09JJ3117)资助项目;国家自然科学基金(编号:50677014;60876022)资助项目

摘　　要：提出了一种基于自适应Chebyshev多项式神经网络(ACNN)的Logistic混沌系统控制算法。该算法采用Chebyshev正交多项式作为神经网络的激励函数,构建Logistic混沌系统的预测与控制模型。为了保证算法的稳定性,提出和证明了收敛定理,并利用自适应学习率算法提高神经网络的学习效率和收敛速度。通过采用自适应Chebyshev神经网络直接学习Logistic混沌系统的动态特性,并对系统实施目标函数控制。实验仿真结果表明,该算法在Logistic混沌系统有外部干扰的情况下仍能对其进行有效控制,网络学习时间为0.178 s,训练步长为10,均方误差达到1.15×10-4,与其他常见算法相比具有计算量小、速度快、精度高和网络结构简单等优点。A novel algorithm for controlling Logistic chaotic system based on adaptive Chebyshev polynomials neural networks（ACNN） is presented.In the algorithm,the activation function of hidden units is defined by Chebyshev orthogonal polynomials in the neural networks,and the forecast and control model of Logistic chaotic system is established.In order to ensure stability of the algorithm,the convergence theorem of the algorithm is proposed and proved.Then the adaptive learning rate algorithm is used for improving the learning efficiency and convergence speed.The adaptive Chebyshev neural networks directly learn dynamic characters of Logistic chaotic system and control it to target function.The simulation results show that the algorithm is still effective when there are external disturbance in the Logistic chaotic system,now the learning time is 0.178s,training steps is 10 and mean square error is 1.15×10-4.Compared with other ordinary algorithms,this algorithm has some merits including significantly little computation,fast convergence speed,high accuracy and simple network structure.

关 键 词：CHEBYSHEV神经网络 自适应学习率算法 收敛定理 Logistic系统 混沌控制 

分 类 号：TP27[自动化与计算机技术—检测技术与自动化装置]